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Match summary
The dominant Edinburgh side surged eight points clear of their Glasgow rivals at the summit of the Scottish Premiership to strengthen their early-season championship claims and deepen the malaise around Brendan Rodgers' side.
Alexandros Kyziridis' fine strike and a spot-kick from Shankland gave Derek McInnes' side a two-goal advantage that the title holders could not overcome.
Dane Murray - among three youth players in the Celtic starting lineup - slashed into his own net early on to put the home side ahead at a energetic their home ground, and it was the youngster's infringement that led to the spot-kick.
Callum McGregor's classy first goal of the season had swiftly equalized the first goal, and the Swedish attacker almost put Rodgers' team in front, choosing placement over power and allowing Alexander Schwolow to make a crucial stop.
But Derek McInnes' irrepressible Hearts regained dominance to consign Celtic to back-to-back losses for the first time since last year.
It also gives the Hearts a commanding advantage at the summit.
The last time they were this far ahead was in 2005-06 under George Burley, when they ended as runners-up - a rare instance that a team has not secured the title after building such an advantage in the last three decades.
McInnes, whose Aberdeen side were second to Celtic on four occasions, has been working hard to play down title talk, as the club seek their first top-flight crown since the 1960s.
The Celtic boss has seen it all before at Celtic - both perfect and shaky beginnings to a season. He's never ended as runner-up.
But on Sunday's evidence, this Edinburgh outfit showed they deserve serious consideration.
Hearts started with the confidence of a side unbeaten in the league this season - fans' favourite Kyziridis delivered a ball for the striker to fire off target.
The Glasgow team didn't help themselves with some uncharacteristic carelessness in possession and they faltered under their initial test.
Claudio Braga's header was touched on to a post by the Celtic keeper and Shankland's return ball was diverted goalwards by the hapless defender, in for the injured Cameron Carter-Vickers.
The away side found their rhythm and started building moves. From one such move, Sebastian Tounekti released the full-back to set up McGregor, who slotted home.
Aside from the Nygren chance, Celtic struggled to create much for striker Kenny or his substitute Yamada amid the unavailability of injured forwards their key strikers.
Hearts rediscovered their energy and adaptability in attacking from across the final third. The Greek forward, a standout performer of the club's scouting network, struck low past the goalkeeper from the just outside the area.
Almost straight away, Murray tripped Braga in the inside right channel and the penalty taker converted. And it could've been an more comprehensive victory, had substitute Ageu not been denied by Schmeichel.
The visitors' performance after the break was somewhat summed up in a couple of moments involving big-money recruit Engles.
The set-piece from Engles delivery was in stark contrast to his European display in the Europa League win over their Austrian opponents and the national team player was then booked for a professional foul.
The Hearts manager: "You see how hard the players work, the togetherness. That's not always enough to win games consistently.
"Our strength lies in, is skillful players. You're seeing that from a lot of players who have been here previously. Recent additions are keen to demonstrate their quality.
"We're in a positive moment at the minute, but it's just one win. It's important for us to maintain this form. We've got loads to do, plenty to improve. Following the initial fixtures is normally an indication of your standing."
Celtic manager Brendan Rodgers: "It's a really poor goal from our perspective. We failed to push up when the play was recycled as a defensive unit so when they play it, they ought to be caught offside but didn't. We have got to improve with the attempt.
"There's still so many points to play for. It's only the beginning. It's just nine matches. Clearly, being eight points behind is not ideal. The comfort is there's so many games to play.
"We now have to focus on the here and now and look to find more consistency and better performance in our play."
The Glasgow club are back at home on Wednesday against promoted side Falkirk (evening kick-off). At the identical hour in the Scottish Premiership, Hearts are at their opponents' ground.
Tech analyst and writer with over a decade of experience in digital transformation and emerging technologies.